a toy rocket is launched into the air. the height, in feet, of the rocket is modeled by the function h(t)=…

a toy rocket is launched into the air. the height, in feet, of the rocket is modeled by the function h(t)= - 16t^2 + 64t + 80, where t is the time, in seconds, that the rocket is in the air. the initial height of the rocket is \n, the rocket reaches a maximum height of \n after \n

a toy rocket is launched into the air. the height, in feet, of the rocket is modeled by the function h(t)= - 16t^2 + 64t + 80, where t is the time, in seconds, that the rocket is in the air. the initial height of the rocket is \n, the rocket reaches a maximum height of \n after \n

Answer

Explanation:

Step1: Find the initial height

The initial height is when (t = 0). Substitute (t=0) into the function (h(t)=- 16t^{2}+64t + 80). [h(0)=-16(0)^{2}+64(0)+80=80]

Step2: Find the time at which maximum height occurs

For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate (in our case (t)) of the vertex is given by (t=-\frac{b}{2a}). Here (a=-16) and (b = 64). [t=-\frac{64}{2\times(-16)}=-\frac{64}{-32}=2]

Step3: Find the maximum height

Substitute (t = 2) into the function (h(t)=-16t^{2}+64t + 80). [h(2)=-16\times(2)^{2}+64\times2 + 80=-16\times4+128 + 80=-64+128+80=144]

Answer:

The initial height of the rocket is 80 feet, the rocket reaches a maximum height of 144 feet after 2 seconds.